Daily Practice · Higher Plus
June 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2020 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2020The probability of winning a game is 4/5. A player expects 8 wins. How many games did they play?
- 2nd June 2020On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd June 2020A rectangle is 29 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th June 2020Work out the coordinates of the turning point of y = x^2 + 4x - 5.
- 5th June 2020y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 6th June 2020In a vector proof you find that vector PQ = 4a - b and vector RS = 16a - 4b. What does this show about PQ and RS?
- 7th June 2020A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 8th June 2020A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 9th June 2020Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 10th June 2020Simplify (x^2 - 12x + 32)/(x - 4).
- 11th June 2020y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
- 12th June 2020A cuboid measures 15 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th June 2020A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th June 2020On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th June 2020A block has mass 600 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th June 2020In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 17th June 2020A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 18th June 2020A cuboid measures 7 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th June 2020A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th June 2020A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 21st June 2020x = 100 and y = 18, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd June 2020Make x the subject of 6x + 8 = y(x + 8).
- 23rd June 2020y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 24th June 2020The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 25th June 2020A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 26th June 2020On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th June 2020A car covers 590 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th June 2020Write 7/(x - 5) + 2/(x + 6) as a single fraction.
- 29th June 2020y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 30th June 2020In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.